Question

The structure shown below will be built for a carnival. The exterior surfaces are going to be painted. What is the total area of the exterior surfaces that need to be painted?

Answer 1

860 square feet of surface needs to be painted.

Explanation:

Answer 2

760 square feet of surface needs to be painted.

Explanation:

Step 1:

To determine the total area of all the exterior surfaces, we need to determine how many external surfaces there are.

For this structure, there are 4 rectangular surfaces and 4 triangular surfaces. The base of the shape will not be painted.

Step 2:

The rectangles have lengths of 10 feet and widths of 12.5 feet.

The area of a rectangle is the product of its length and its width.

The area of a rectangular surface
`= (10)(12.5) = 125` square feet.

The area of 4 such rectangular surfaces
`= 4(125) = 500` square feet.

Step 3:

The triangles have base lengths of 10 feet and heights of 13 feet.

The area of a triangle is half the product of its base length and its height.

The area of a triangular surface
`=(1)/(2) (10)(13) = 65` square feet.

The area of 4 such triangular surfaces
`= 4(65) = 260` square feet.

Step 4:

The total surface area is the sum of all the external surfaces.

The total surface area
`= 500 + 260 = 760` square feet.

So 760 square feet of surface needs to be painted.